The present invention relates in general to three-dimensional (3-D) display of tomographic data, and more specifically to forming 3-D images from a tomographic data set in which a surface is defined by a variable threshold.
Tomographic medical imaging employs the collection of data representing cross sections of a body. A plurality of object interrogations can be processed mathematically to produce representations of contiguous cross-sectional images. Such cross-sectional images are of great value to the medical diagnostician in a non-invasive investigation of internal body structure. The technique employed to collect the data can be x-ray computed tomography, nuclear magnetic resonance tomography, single-photon emission tomography, positron emission tomography, or ultrasound tomography, for example.
A body to be imaged exists in three dimensions. Tomographic devices process data for presentation as a series of contiguous cross-sectional slices along selectable axes through the body. Each cross-sectional slice is made up of a number of rows and columns of voxels (parallelopiped volumes with certain faces corresponding to pixel spacing within each slice and others corresponding to slice spacing), each represented by a digitally stored number related to a computed signal intensity in the voxel. In practice, an array of, for example, 64 slices may each contain 512 by 512 voxels. In normal use, a diagnostician reviews images of a number of individual slices to derive the desired information. In cases where information about a surface within the body is desired, the diagnostician relies on inferences of the 3-D nature of the object derived from interrogating the cross-sectional slices. At times, it is difficult or impossible to attain the required inference from reviewing contiguous slices. In such cases, a synthesized 3-D image would be valuable.
Synthesizing a 3-D image from tomographic data is a two-step process. In the first step, a mathematical description of the desired object is extracted from the tomographic data. In the second step, the image is synthesized from the mathematical description.
Dealing with the second step first, assuming that a surface description can be synthesized from knowledge of the slices, the key is to go from the surface to the 3-D image. The mathematical description of the object is made up of the union of a large number of surface elements (SURFELS). The SURFELS are operated on by conventional computer graphics software, having its genesis in computer-aided design and computer-aided manufacturing, to apply surface shading to objects to aid in image interpretation through a synthesized two-dimensional image. The computer graphics software projects the SURFELS onto a rasterized image and determines which pixels of the rasterized image are turned on, and with what intensity or color. Generally, the shading is lightest (i.e., most intense) for image elements having surface normals along an operator-selected line of sight and successively darker for those elements inclined to the line of sight. Image elements having surface normals inclined more than 90 degrees from the selected line of sight are hidden in a 3-D object and are suppressed from the display. Foreground objects on the line of sight hide background objects. The shading gives a realistic illusion of three dimensions.
Returning now to the problem of extracting a mathematic description of the desired surface from the tomographic slice data, this step is broken down into two subtasks, namely the extraction of the object from the tomographic data, and the fitting of a surface to the extracted object. A number of ways are available to do the first subtask. For example, it is possible to search through the signal intensities in the voxels of a slice to discern regions where the material forming the object has sufficient signal contrast with surrounding regions. For example, signal intensities characteristic of bone in x-ray computed tomography have high contrast with surrounding tissue. A threshold may then be applied to the voxels to identify each one in the complete array lying in the desired object from all voxels not in the object.
Referring now to the second subtask, one technique for fitting a 3-D surface to the extracted object is known as the dividing cubes method which is disclosed in commonly assigned U.S. Pat. No. 4,719,585, issued Jan. 12, 1988, which is hereby incorporated by reference. By the dividing cubes method, the surface of interest is represented by the union of a large number of directed points. The directed points are obtained by considering in turn each set of eight cubically adjacent voxels in the data base of contiguous slices. Gradient values are calculated for these large cube vertices using difference equations. The vertices are tested against a threshold to determine if the surface passes through the large cube. If it does, then the large cube is subdivided to form a number of smaller cubes, referred to as subcubes or subvoxels. By interpolation of the adjacent point densities and gradient values, densities are calculated for the subcube vertices and a gradient is calculated for the center of the subcube. The densities are tested (e.g., compared to the threshold). If some are greater and some less than the threshold, then the surface passes through the subcube. In that case, the location of the subcube is output with its normalized gradient, as a directed point. It is also possible to define a surface using a range of densities (e.g., an upper and a lower threshold). Thus, where thresholds are mentioned herein, a range is also intended to be included. The union of all directed points generated by testing all subcubes within large cubes through which the surface passes, provides the surface representation. The directed points are then rendered (i.e., rasterized) for display on a CRT, for example.
In displaying a 3-D image of particular objects, it has been found that an image artifact can arise such that part of a structure is missing. For example, in generating a 3-D image of a skull using the dividing cubes method as described above, the top areas of the skull may drop out of the image. This dropping out has been found to be caused by a partial volume effect. Thus, where the object surface of interest tends toward being much less than the thickness of the acquired slices, each voxel can contain both bone (high CT density) and air or soft tissue (low CT density). The resulting CT number for the voxel is then of an intermediate CT density. Such voxels with a reduced density number are not extracted by the surface generator since their density is below the threshold used to extract the bone. If the threshold is lowered to account for the lower density voxels, increased noise will degrade the final image.
Accordingly, it is a principal object of the present invention to provide a method and apparatus for generating 3-D images of tomographic data without partial volume artifacts.
It is another object to extract 3-D surface definitions with reduced noise using a dividing cubes method.